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A Concentric Plasmonic Platform for the Efficient Excitation of Surface Plasmon-Polaritons

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A Concentric Plasmonic Platform for the Efficient Excitation of Surface Plasmon-Polaritons A concentric plasmonic platform for the efficient excitation of surface plasmon-polaritons Nancy Rahbany1, Wei Geng1, Rafael Salas-Montiel1, Sergio de la Cruz2, Eugenio R. Méndez2, Sylvain Blaize1, Renaud Bachelot1, Christophe Couteau1,3,4* 1 Laboratory of Nanotechnology, Instrumentation and Optics, ICD CNRS UMR 6281, University of Technology of Troyes, 10000, Troyes, France 2 División de Física Applicada, Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No. 3918, Ensenada 22860, BC, México 3 CINTRA CNRS-Thales-NTU, UMI 3288, Research Techno Plaza, 50 Nanyang Drive, Singapore 4 Centre for Disruptive Photonics Technologies (CDPT), Nanyang Technological University, Singapore *Correspondence and requests for materials should be addressed to C.C. (email: [email protected]). Abstract: We propose a plasmonic device consisting of a concentric ring grating acting as an efficient tool for directional launching and detection of surface plasmon-polaritons (SPPs). Numerical simulations and optical characterizations are used to study the fabricated structured gold surface. We demonstrate that this circularly symmetrical plasmonic device provides an efficient interface between free space radiation and SPPs. This structure offers an excellent platform for the study of hybrid plasmonics in general and of plasmon-emitter couplings in particular, such as those occurring when exciting dye molecules placed inside the ring. As illustrated in this work, an interesting property of the device is that the position of excitation determines the direction of propagation of the SPPs, providing a flexible mean of studying their interactions with molecules or dipole-like emitters placed on the surface. There is a growing interest nowadays in the study of light-matter interaction at the nanometer scale [1]. Using plasmonics, nanooptics and metamaterials, there is an important drive towards enhancing such an interaction. For instance, upon integrating single-photon sources with plasmonic structures, the emitter’s enhanced Purcell factor in the weak coupling regime can be obtained [2, 3]. In plasmonics, researchers have proposed methods and devices that allow the understanding of SPP launching and propagation such as nanoslit arrays [4], metal and dielectric strips and wires [5, 6], carbon nanotubes [7], metallic nanowires [8, 9], metallic nanoparticles [10] and dislocated double-layer metal gratings [11]. Recent work has been done on combining quantum optics and plasmonics by studying the transmission of entangled photons between two metallic gratings upon exciting single waveguided SPPs [12]. The same platform can be used as an efficient nanoscale focusing device [13–15] as well as a confined surface plasmon polariton amplifier [16]. Plasmonic lenses made of concentric annular rings, known as bull’s eye nanoantennas, have shown to increase the electric field enhancement and confinement [17, 18] and to control the emission direction of molecules placed in the center [19]. Furthermore, studies on integrating optical antennas into concentric ring gratings show that the field enhancement and coupling efficiency can be improved, as well as the fluorescent enhancement of emitters placed inside the ring-antenna system [20, 21]. Moreover, in order to get efficiently excited, dipole emitters must have a specific orientation with respect to the incident light polarization giving rise to a specific emission radiation pattern [22, 23]. There is thus an advantage in using a configuration that, unlike bull’s eye nanoantennas, studies the behavior of propagating SPPs which can be used to excite emitters regardless of the emitters’ orientation. Reciprocally, it would be useful if this structure would allow excited emitters placed inside it to generate SPPs that propagate and then reradiate in the far field out-coupling regardless of where they are located [21,22]. This is precisely what our present work intends to do by studying the excitation of SPPs with a specially fabricated ring grating structure. We demonstrate the interaction of these surface waves with fluorescent emitters placed inside the ring which makes our device useful in measuring the SPP emission direction. We also show that the generated SPPs propagate with a specific wave vector in a specific direction and exciting the ring grating from different positions leads to SPP orientation in a precise desired direction. The article is organized as follows: The second section describes the design of the structures to couple a propagating beam of light into SPPs (“Design of the Structures” section). In “Experimental Results and Discussion” section, we present details of the fabrication and experimental results on the excitation and propagation of SPPs with the proposed structures. We also show the excitation of dye molecules by SPPs and the excitation of SPPs by the fluorescence of dye molecules using our plasmonic device. Finally, the last section contains our main conclusion (“Conclusion” section). We demonstrate that the proposed device can be used to study and control plasmon-emitter interactions, making the structure a convenient plasmonic platform. Design of the Structures In this section we present the procedure employed to design the structures and provide a brief description of the numerical approach used in this process, and in the evaluation of their performance. Our structure is composed of a circular ring grating that provides a useful platform for focusing SPPs in its center where the wave amplitude reaches its maximum [14]. This allows studying SPP properties and their interactions with emitters and absorbers. A schematic illustration of the situation considered is illustrated in Fig. 1. If the radius of curvature of the rings is much greater than the diameter of the illuminating beam, the situation can be well approximated by the geometry of a linear grating assumed in the following calculations. We start by considering the generic geometry illustrated in Fig. 2. A profile Γ defines the interface between a metal with dielectric constant εm(ω) and air, with index of refraction n0=1.We assume that the surface is invariant along z and that the illumination is provided by a monochromatic beam of light propagating on the xy-plane. Under the assumed conditions, for purely s- or p-polarized incident waves, the state of polarization is retained after interaction with the surface, and the two polarization modes may be treated independently. Since our primary interest is the excitation of SPPs, we only consider the case of p-polarization. Since in this case the magnetic field vector is along the z- direction, the problem is most naturally solved in terms of this component, which we represent by H (x,y). We now provide a brief description of the numerical method employed to solve the problem. More details can be found in Refs. [24, 25]. We use the Green's integral theorem and consider the total field above the surface as being the sum of the incident and scattered fields. By solving a set of integral equations [24, 25], we can then deduce the surface field. Once the surface field is found, it is straightforward to calculate the excitation efficiency. For this, let us consider the field associated with an SPP originating at x = 0, with amplitude H0, traveling on a flat surface in the direction +x. This field can be expressed in the form (0) ikSPP x0 y H(r ) H0 e y 0, (1) ()m ikSPP x m y H(r ) H0 e y 0, (2) for x > 0. Here, 0 m kkSPP 0 (3) 0 m is the wavenumber of the SPPs, and 2 j j k0 (4) 0 m is the decay constant of the field in the two media. In this last expression, the sub-index j = 0 for free-space or j = m for metal, and k0 = ω/c is the free-space wavenumber. Evaluating the component of the Poynting vector that crosses the plane x = 0, and integrating along y, we find that [26] 2 2 ()j c Hk0 SPP Pxz L e, (5) 8 2 ' jj where βj' = Re{βj}, Lz is a length along the z direction and, again, j refers to air or metal. Considering now a situation in which the SPP has been excited by the interaction between an illuminating beam and a surface feature, one can define the excitation efficiency as (0) (m ) PPxx (6) Pinc where Pinc is the power of the incident beam. To design a coupling structure, we begin by considering the excitation efficiency that can be achieved with a sub- wavelength rectangular groove ruled on a metal surface. This efficiency is closely related to its electromagnetic resonances [27]. Once a suitable width and depth have been chosen, we consider a sequence of N such groves placed in a regular grid, choosing the period d in such a way that the SPPs excited by them interfere constructively. This means that the periodicity of the grating must be such that the following matching equation is satisfied kSPP n00 ksin qk g (7) where kg = 2π/d is the grating wavenumber, and q is an integer. To maximize the efficiency, and reduce the effects of stray light, it is convenient to choose a period that is smaller than the wavelength. In such circumstances, apart from the specular order, the grating produces no propagating orders for small angles of incidence. For a wavelength of 980 nm and a period of 800 nm, for example, Eq. (7) predicts that the coupling condition is reached when θ is about -10o. Long gratings, however, do not couple efficiently to freely propagating SPPs [26, 27]. This is because, as the coupled SPPs propagate through the grating, they are diffracted by the grating and radiate into air and the metal. Through numerical studies with a variable number of grooves, we have found that there is practically no improvement of the efficiency after five grooves [27]. The designed couplers consist then of five grooves. The inset of Fig. 3 shows a schematic diagram of the grating coupler.
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